POST UTME UI 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )
B. \( \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \ \) )
C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )
D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )
Question 2
Evaluate the integral \int_0^1 x^2 \ln x \, dx.
A. \frac{1}{3} - \frac{1}{4}
B. \frac{1}{2} - \frac{1}{3}
C. \frac{1}{3} + \frac{1}{4}
D. \frac{1}{2} + \frac{1}{3}
Question 3
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{3pi}{2} \)
C. \( x = \frac{pi}{4} \) and \( x = \frac{3pi}{4} \)
D. \( x = \frac{pi}{4} \) and \( x = \frac{5pi}{4} \)
Question 4
Solve the system of linear equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \\begin{bmatrix} 1 \\ 2 \\end{bmatrix}
B. \\begin{bmatrix} 2 \\ 1 \\end{bmatrix}
C. \\begin{bmatrix} 3 \\ 4 \\end{bmatrix}
D. \\begin{bmatrix} 4 \\ 3 \\end{bmatrix}
Question 5
Solve the system of equations u\sing matrices:\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} \)
B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix} \)
C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \)
D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} \)
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 7
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is red?
A. \frac{1}{2}
B. \frac{2}{3}
C. \frac{5}{8}
D. \frac{3}{4}
Question 8
Find the volume of the sphere \( V = \frac{4}{3} pi r^3 \) if the radius is 6 cm.
A. 904.778
B. 904.779
C. 904.780
D. 904.781
Question 9
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).
A. x^2 + y^2 - 6x - 4y + 12 = 0
B. x^2 + y^2 - 8x - 2y + 16 = 0
C. x^2 + y^2 - 4x - 6y + 20 = 0
D. x^2 + y^2 - 2x - 4y + 8 = 0
Question 10
Find the equation of the circle with center ( (3, 4) ) and radius 5.
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25
B. \( x - 4 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 3 \)^2 + \( y - 4 \)^2 = 30
D. \( x - 4 \)^2 + \( y - 3 \)^2 = 30
Question 11
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{5}
D. \frac{2}{3}
Question 12
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the chain rule.
A. 6x + 2
B. 3x^2 + 2
C. 6x - 2
D. 3x^2 - 2
Question 13
Solve the equation \( x^2 + 2x - 6 = 0 \).
A. \( -3, 2 \)
B. \( -2, 3 \)
C. \( 1, -2 \)
D. \( -1, 2 \)
Question 14
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}} )
B. ( f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}} )
C. ( f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}} )
D. ( f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}} )
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2}{x^3} )
B. ( f'(x) = \frac{2}{x^3} )
C. ( f'(x) = \frac{-1}{x^3} )
D. ( f'(x) = \frac{1}{x^3} )

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